Inquiry Project Update

So, in attempting to write with a more formal tone, I made my first draft very, very devoid of my voice. Which is frustrating. But I’m going back and fixing it. And hey, that’s what drafting is for.

Also, trying to make sure I weave a story in with my argument. And weave my argument into my paper, just to make sure it is tying together for readers, because I know what I’m trying to say, but that doesn’t mean everyone will know what I’m trying to say.

Focus!

I am researching how mathematics in public education can be changed in a way that reflects the true nature of mathematics as an art form.  A strong foundation in mathematics would allow students to learn how to problem solve effectively and think critically.  Neurologically, the brain is most effective at learning (and learning how to learn) in adolescence. Seeing as mathematics is a discipline of reasoning, it makes sense to alter the way mathematics is taught to encourage mental growth.

Sources:

Bereday, George Z. F., and Luigi Volpicelli. “Philosophical Theories of American Education.” Public education in America; a new interpretation of purpose and practice,. . Reprint. New York: Harper, 1958. . Print.

“Federal Role in Education.” Federal Role in Education. N.p., n.d. Web. 21 July 2014. <http://www2.ed.gov/about/overview/fed/role.html>.

Bass, Randall V.. “The Purpose Of Education.” The Educational Forum: 128-132. Web. 22 July 2014.
Hardy, G. H., and C. P. Snow. A mathematician’s apology,. ed. London: Cambridge U.P., 1967. Print.

Lockhart, Paul. A mathematician’s lament. New York, NY: Bellevue Literary Press, 2009. Print.

Purcell, Andrew. “Brain’s synaptic pruning continues into your 20s.” New Scientist: 9. Web. 22 July 2014.

Kostovic, I., M. Judas, and Z. Petanjek. “Extraordinary neoteny of synaptic spines in the human prefrontal cortex.” Proceedings of the National Academy of Sciences: 13281-13286. Web. 22 July 2014.

Klein, David. “A Brief History of American K-12 Mathematics Education in the 20th Century .” Mathematical Cognition. : Information Age Publishing Inc, 2003. . Print.

Progress!

Just an update!

I’ve been organizing sources so to make sure they are included in an orderly fashion that answers the questions I need to answer in a logical order.

Also I have been writing! First draft is close to being done.

So just remember

(even more so when you back them up with expert sources)

 

Also, the Alan Turing movie that’s coming out is gonna be awesome.

 

And as always

Research reflection. Framing and Drafting.

This week has been hectic! Family vacations are fun, but stressful.

I think I need to draw a line with the amount of sources I have now! I’ve collected a ton a good information from good places, and there is still a lot out there. But I need to finish framing my ideas and sources into a conversation so that I can come up with a good preliminary draft! Due dates are approaching…scary.

Good luck everyone!

That’s so Meta – Concept Experience #5

So I’m not sure that all of these posts “clearly demonstrate the use of personal, interactive, networked computing as a “metamedium,” as something with “unanticipated” or surprising uses.” However, most of them can relate to the use of such a metamedium since they are mostly theoretical concepts on how the way math is taught could be changed.

MATH IS ART

After reading Lockhart’s Lament I was inspired by his work and his initial analogy of the current state of mathematics education in which he details the nightmares of an artist and a musician (I recommend reading the first  page of his paper) who’s art forms have been reduced and taught to public school students who learned paint-by-numbers and complex musical theory. And they both wake up scared that their beautiful art forms had been reduced “to something mindless and trivial”.

So the idea of modelling a math class like an art class struck me as ideal. I began researching art class curriculum, and not surprisingly, I found very little. There wasn’t much structure and not many planned lesson plans available to teachers. And the lesson plans I did find online (which were more like general descriptions for each grade) were very broad, very abstract, and left room for teachers to let the students explore and learn through exploration.

This also led me to the question, who teaches art classes? ARTISTS! Who teaches mathematics? Hint: probably not mathematicians.

So all of this brought me to ask the questions, how can we make math class more like art class?

 

LET THEM EAT PROOFS

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A proof from a case study of a young girl who began proving her work in 1st grade.

Inspired again by Lockhart’s Lament along with many other sources that talked about students ability to prove their work, and in proving their work they would better learn and understand concepts behind mathematics. One of my favorite examples is the 3-act format lesson plan-one which I think could be implemented as long term projects in classrooms. A video introduction of them problem followed by group work and problem solving where students come up with their own unique explanations and solutions to problems.

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The power of a video problem really interested me, because it allows students to visualize the problems, even outside of class, and then discover and explore on their own. Even just getting them to think about the question before coming to class could get students thinking and ready for interactive learning.

 

INQUIRY PROPOSAL – SECOND DRAFT

Specifically the “My Project In The Concept Space Of The Web” section.

I take a lot in inspiration for the type of paper I want to write from NPR. The way they represent their ideas with video, sound, hyperlinks and text combined is a super effective way to communicate ideas (and NPR is just cool.)

So I think that using this style of representation for my own ideas will be a great way to relay information and opinion. (side note, have you heard the bad costumer service call yet? If not, listen.)

This is not really a way I used a metamedium, but a way I will use a metamedium for my final project!

Collecting sources, framing ideas.

Today I read over more responses to my survey and started compiling them into lists.

Also looking at more studies about education and math and problem solving and how they all intertwine.

For an updated list on online sources I’ve been looking at, check out my Diigo!

And for a fun math problem/proof to solve, try this:

Assume you have a chocolate bar consisting, as usual, of a number of squares arranged in a rectangular pattern. Your task is to split the bar into small squares (always breaking along the lines between the squares) with a minimum number of breaks. How many will it take?

Solution is here!

Survey anyone?

Today I wanted to start with some interviewing processes, do a brief opinion poll to figure out what people think about education!

I was a little worried about the fact that I would be sharing this survey on facebook and twitter, and that a lot of my friends are engineering majors so the data would be skewed! But I ended up with a really wide range of people, from people who studied cosmetology to people who studied geology, and pretty much everywhere in between that.

I asked some basic questions, about level of schooling and the major focus of study, and then I asked people to rank topics they studied in primary school. As of now the list goes like this:

Science > English > Extracurricular Activities > History > Math > Foreign Languages > Geography

I am curious to know why science has pulled out on the top for most of these people (this is why I need another survey, oops). But if I had to guess (which I shouldn’t guess, but I am going to take it from personal experience) it is because of the hands on learning. Science lab was always a lot of fun! We might be building an egg drop container or a car, or making some fun chemical reaction! Hands on learning was always a blast.

(g)old

I still need to gather all of the responses from my other questions together and find some common themes, but from browsing them it looks like people generally want to see education teach people how to think, help them to explore their interests and talents, prepare them for “the real world”, to stop “teaching to the test” and stop teaching to the slowest learner in the classroom.

Tell me your opinions here!

Personal Dynamic Media – Nugget #5

First of all, this is how I feel about Monday’s, even summer Monday’s, they are just always a drag and I’m not sure why. Conditioning maybe?
          “Considering children as the users radiates a compelling excitement when viewed from a number of different perspectives. First, the children really can write programs that do serious things. Their programs use symbols to stand for objects, contain loops and recursions, require a fair amount of visualization of alternative strategies before a tactic is chosen, and involve interactive discovery and removal of “bugs” in their ideas.
            Second, the kids love it! The interactive nature of the dialogue, the fact that they are in control, the feeling that they are doing real things rather than playing with toys or working out “assigned” problems, the pictorial and auditory nature of their results, all contribute to a tremendous sense of accomplishment to their experience. Their attention spans are measured in hours rather than minutes.”
While reading the article I just kept thinking to myself ‘we can do this, and this, and this.’ A lot of Kay and Goldberg’s ideas have been implemented already. But what I don’t see being implemented are their ideas about how inclusive and wide-reaching the access to this technology and knowledge of how to use it should be. And even more specifically, that children are not taught to use these things even though they are more than capable.
There is actually a movement towards teaching people how code in schools. A new school in France called École 42 has no teachers, no books, no tution, and it’s sole purpose is to give people the opportunity to learn how to program. And kids can certainly be taught to code from a young age, even if it isn’t traditional coding like C++
Different commands can be represented by symbols and students would learn the ideas and how to think about programming before being introduced to actual programming. Many problems arise with teaching programming in class (some detailed here). But they don’t have to do with children’s ability to learn and understand, they have to do with funding, teachers, how to count the credits, and so on.
Overall, teaching children how to program would be beneficial to their problem solving skills, and beneficial to a world in the future that is even more inundated with technology (which is almost hard to imagine).

Reflection #4

(late…oops)

The past week I was very productive in defining and narrowing my research topic. I was also ENTIRELY OVERWHELMED with sources. But it was a good thing, because it gave me a lot of exposure to a lot of different ideas within my topic that I need to understand.

I was able to get some twitter networking done (twitter networking? oh yeah.) and talk to David Coffey,  a math professor from Michigan who focuses on changing the way math is taught! So that is another step towards having some of my own interviews and gathering some of my own expert data before I write.

I am trying to reach out to classmates, and give them thoughtful comments that will give them new ideas about their inquiry! So hopefully that will lead to more meaningful discussions later with people who have been keeping up with my work as well.

Everything is going really well, and I’m excited about another week of learning!

Let them eat proofs

What I have researched today (and new sources):

I think mathematical proofs are really misjudged. When I think of a proof, I automatically think of something like this:

When really they can be as simple as this:

An example of a simple proof from Lockhart’s Lament.

Every rule that you memorized in math has a proof behind it-and a lot of these proofs are really just an exercise in critical thinking. Not anything long and complicated. And I don’t mean necessarily any sort of formal proof, but a proof that a seven year old could come up with.

For instance, I’m sure that everyone had to memorize sign conventions in multiplication, and so you learned that a positive and a positive make a positive, a positive and a negative make a negative and a negative and a negative make a positive. I never really understood that concept, and it took me a while to memorize it because I didn’t understand the reasoning! (part of the reason I went into remedial math I think.) So I ask you reader, why do you get a positive when you multiply two negatives?

Don’t feel bad if you didn’t get it, I didn’t either. In fact, I didn’t even question this convention, I just learned it and I’ve used it ever since. And I didn’t think about it until I read this article.  But here is a basic proof for why it is how it is from Khan Academy.

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What better way to learn is there than teaching yourself? And that is very simple arithmetic, just takes a bit of creative thinking to come up with something similar on your own, and once you spend enough time trying to figure something out on your own-you usually aren’t prone to forgetting it.

I think the skill of proof writing can be introduced much earlier than it is now (I never once did proofs in high school), and it is a critical part of true mathematics. So why not start teaching real, creative mathematics to students sooner?

Relearning how to learn